Sea level prediction using ARIMA, SVR and LSTM neural network: assessing the impact of ensemble Ocean-Atmospheric processes on models’ accuracy

Figures & data

Table 1. Input variables considered in some existing studies of sea level prediction around East Asian sea.

Author	Stations	Models	Input Variables	Performance On test data (R)
Lai et al. (2019)	Kerteh, Tioman Island, Tanjung Sedili (Malaysia)	SVR, Genetic Programming (GP)	3 variables; Precipitation, Cloud cover, sea surface temperate	Between 0.728 − 0.863
Muslim et al. (2020)	Kudat, Sandakan, Kota Kinabalu (Malaysia)	MLP-ANN, ANFIS	4 variables; Wind direction, wind speed, rainfall, cloud cover	Between 0.7223 − 0.8274
Eun-Joo et al. (2020)	Pohang, Tongyeong, Moseulpo, Jin-do, Anheung (Korea)	LSTM neural network	4 variables- Precipitation, wind speed, sea surface temperature, barometric pressure	Above 0.85
Lai et al. (2020)	Kerteh, Tanjung Sedili, Tioman Island (Malaysia)	SVR	3 variables – sea surface temperature, rainfall, cloud cover	Between 0.825 and 0.861

Figure 1. Map of the Malaysia Sea showing Malacca strait and the locations of West Peninsular tide gauges. Source: Author.

Figure 2. Elevation profile of West Peninsular Coastline.

Table 2. Tide gauge stations at the West Peninsular Malaysia.

Station ID	Station name	Region	Established	LAT	LON	% completeness	Near GNSS Station
1676	Pulau Langkawi	Penninsular (North West)	1986	6.431	99.764	96	No
1595	Pulau Pinang	Penninsular (North West)	1985	5.422	100.347	93	No
1594	Lumut	Penninsular (North West)	1984	4.240	100.613	93	No
1591	Port Kelang	Penninsular (West Central)	1984	3.050	101.358	90	No
1593	Tanjung Keling	Penninsular (West Central)	1984	2.215	102.153	94	GPS MELAKA (JUML)
1677	Kukup	Penninsular (South West)	1986	1.325	103.443	97	No
248	Johor Bahru	Penninsular (South West)	1984	1.462	103.792	91	No

Figure 3. Heat Map of ocean-atmosphere variable correlation matrix for Johor Bahru.

Table 3. Summary Statistics of the ocean-atmosphere variables for 7 stations in West Peninsular Malaysia.

Station name	Statistics	SLA (m)	SST (^oC)	SSS (0.001)	SSD (kg/m^3)	Wind Speed (ms-1)	Surface AP (hPa)	Cloud Cover	Precipitation (m)
Pulua Langkawi	mean	0.0361	29.63	31.95	1019.73	3.15	100786	0.78	0.0060
	std	0.0771	0.79	0.41	0.14	0.77	89.8845	0.13	0.0036
	min	−0.1882	27.57	30.64	1019.31	1.81	100547	0.38	0.0001
	max	0.2458	31.47	32.64	1020.05	5.76	101025	0.96	0.0171
Pulau Pinang	mean	0.0417	29.60	31.32	1021.10	2.22	100779	0.81	0.0069
	std	0.0770	0.64	0.57	0.18	0.34	84.1862	0.11	0.0032
	min	−0.1759	28.43	30.20	1020.43	1.66	100550	0.45	0.0008
	max	0.2548	30.93	32.16	1021.50	3.98	101020	0.96	0.0186
Lumut	mean	0.0451	29.72	31.71	1019.55	2.64	100945	0.83	0.0074
	std	0.0800	0.50	0.49	0.14	0.45	84.2292	0.09	0.0030
	min	−0.2035	28.20	29.78	1019.01	1.70	100715	0.49	0.0016
	max	0.2657	31.06	32.49	1020.00	4.37	101185	0.96	0.0187
Port Kelang	mean	0.0406	29.60	31.76	1019.64	2.90	100814	0.82	0.0079
	std	0.0791	0.60	0.47	0.16	0.53	83.1363	0.09	0.0033
	min	−0.1582	27.83	29.40	1019.00	1.88	100579	0.48	0.0009
	max	0.2441	31.06	32.42	1020.08	4.97	101045	0.96	0.0214
Tanjung Keling	mean	0.0369	29.41	31.63	1019.73	2.70	100560	0.82	0.0064
	std	0.0746	0.79	0.52	0.25	0.54	83.4715	0.08	0.0026
	min	−0.1187	27.07	28.63	1019.20	1.76	100315	0.52	0.0002
	max	0.2511	31.26	32.59	1020.28	4.72	100783	0.97	0.0241
Kukup	mean	0.0300	29.18	30.75	1019.81	3.62	100916	0.80	0.0065
	std	0.0736	0.82	0.63	0.33	0.72	83.2241	0.09	0.0026
	min	−0.1399	27.75	29.38	1019.32	2.23	100668	0.48	0.0001
	max	0.2440	30.47	31.57	1020.51	5.51	101134	0.95	0.0165
Johor Bahru	mean	0.0327	29.16	30.73	1019.81	2.39	100632	0.81	0.0073
	std	0.0870	0.76	0.62	0.33	0.54	83.1663	0.08	0.0028
	min	−0.1520	27.61	29.28	1019.32	1.45	100384	0.51	0.0006
	max	0.2862	31.04	31.55	1020.51	3.95	100852	0.96	0.0157

Figure 4. Time series analysis plots for Johor Bahru showing (a) sea level decomposed into trends, seasonality and residuals. (b) rolling mean statistics (c) autocorrelation (d) Partial autocorrelation.

Figure 5. Heat map of ocean-atmosphere correlation for Johor Bahru (a) and Lumut (b).

Table 4. Correlation of ocean-atmospheric variables with sea level.

	Sea Temperature	Sea Salinity	Sea Surface Density	Wind Speed	Surface AP	Cloud Cover	Precipitation
Pulua Langkawi	0.043	−0.01	−0.026	0.0085	−0.027	0.47	0.28
Pulau Pinang	0.11	−0.053	−0.35	0.19	−0.25	0.45	0.25
Lumut	−0.016	−0.14	−0.31	0.29	−0.29	0.44	0.14
Port Kelang	0.083	−0.31	−0.41	0.21	−0.25	0.42	0.28
Tanjung Keling	−0.0083	−0.3	−0.17	0.2	−0.083	0.41	0.079
Kukup	−0.24	−0.063	0.24	0.14	0.049	0.44	0.0042
Johor Bahru	−0.31	0.13	0.45	0.3	0.15	0.42	0.23

Table 5. R accuracy of ARIMA, SVR and LSTM models for different scenarios at all station.

	ARIMA	SVR					LSTM
Station	No input	OV	AV	OAV	% Increase of AV relative to OV	% Increase of OAV relative to AV	OV	AV	OAV	%Increase of AV relative to OV	% Increase of OAV relative to AV
Langkawi	0.882	0.591	0.749	0.769	21.095	2.601	0.637	0.839	0.879	24.076	4.768
Pinang	0.605	0.549	0.726	0.742	24.380	2.156	0.595	0.816	0.852	27.083	4.412
Lumut	0.683	0.626	0.679	0.718	7.806	5.432	0.672	0.769	0.828	12.614	7.672
Port Kelang	0.835	0.699	0.659	0.712	−6.070	7.444	0.745	0.749	0.822	0.534	9.746
Tanjung Keling	0.703	0.619	0.706	0.737	12.323	4.206	0.665	0.796	0.847	16.457	6.407
Kukup	0.573	0.521	0.743	0.769	29.879	3.381	0.567	0.833	0.839	31.933	0.720
Johor Bahru	0.692	0.575	0.776	0.792	25.902	2.020	0.621	0.866	0.902	28.291	4.157
Mean of R	0.710	0.597	0.720	0.748	16.474	3.891	0.643	0.810	0.853	20.141	5.412

*OV, Ocean variables; AV, Atmospheric Variables; OAV, Ocean Atmospheric variables.

Figure 6. Relative SLA pattern for North West Peninsular.

Figure 7. Relative SLA pattern for West Central Peninsular.

Figure 8. Relative SLA pattern for South West Peninsular.

Table 6. Relative Sea Level Trend of the seven tide gauge stations at West Peninsular.

Location	Rate by Robust Fit (mm/yr)	Min			Max		Mean
		Date	Value		Date	Value
Pulau Langkawi	4.14 $\pm$2.20	12/1997		−272	10/2010	295	56.5
Pulau Pinang	4.04 $\pm$2.40	12/1997		−299	10/2010	265	20.4
Lumut	3.31$\pm$ 1.88	01/1998		−189	06/2016	311	54.87
Port Kelang	3.80$\pm$ 2.46	12/1997		−284	10/2010	210	−17.5
Tanjung Keling	3.07 $\pm$2.07	03/2005		−184	10/2010	207	1.0
Kukup	5.90 $\pm$ 1.86	03/2005		−118	12/2017	294	55.9
Johor Bahru	3.88 $\pm$2.67	06/1993		−147	12/2011	352	41.4

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